<h2>Problem 108</h2>
<div style="color:#666;font-size:80%;">04 November 2005</div><br />
<div class="problem_content">
<p>In the following equation <var>x</var>, <var>y</var>, and <var>n</var> are positive integers.</p>
<div style="text-align:center;">
<table align="center">
<tr>
<td><div style="text-align:center;">1<br /><img src="images/blackdot.gif" width="15" height="1" alt="" /><br /> <var>x</var></div></td>
<td> + </td>
<td><div style="text-align:center;">1<br /><img src="images/blackdot.gif" width="15" height="1" alt="" /><br /> <var>y</var></div></td>
<td> = </td>
<td><div style="text-align:center;">1<br /><img src="images/blackdot.gif" width="15" height="1" alt="" /><br /> <var>n</var></div></td>
</tr>
</table>
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<p>For <var>n</var> = 4 there are exactly three distinct solutions:</p>
<div style="text-align:center;">
<table align="center">
<tr>
<td><div style="text-align:center;">1<br /><img src="images/blackdot.gif" width="15" height="1" alt="" /><br /> 5</div></td>
<td> + </td>
<td><div style="text-align:center;">1<br /><img src="images/blackdot.gif" width="15" height="1" alt="" /><br /> 20</div></td>
<td> = </td>
<td><div style="text-align:center;">1<br /><img src="images/blackdot.gif" width="15" height="1" alt="" /><br /> 4</div></td>
</tr>
<tr>
<td><div style="text-align:center;">1<br /><img src="images/blackdot.gif" width="15" height="1" alt="" /><br /> 6</div></td>
<td> + </td>
<td><div style="text-align:center;">1<br /><img src="images/blackdot.gif" width="15" height="1" alt="" /><br /> 12</div></td>
<td> = </td>
<td><div style="text-align:center;">1<br /><img src="images/blackdot.gif" width="15" height="1" alt="" /><br /> 4</div></td>
</tr>
<tr>
<td><div style="text-align:center;">1<br /><img src="images/blackdot.gif" width="15" height="1" alt="" /><br /> 8</div></td>
<td> + </td>
<td><div style="text-align:center;">1<br /><img src="images/blackdot.gif" width="15" height="1" alt="" /><br /> 8</div></td>
<td> = </td>
<td><div style="text-align:center;">1<br /><img src="images/blackdot.gif" width="15" height="1" alt="" /><br /> 4</div></td>
</tr>
</table>
</div>
<p>What is the least value of <var>n</var> for which the number of distinct solutions exceeds one-thousand?</p>
<p class="info">NOTE: This problem is an easier version of problem <a href="index.php?section=problems&amp;id=110">110</a>; it is strongly advised that you solve this one first.</p>
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